A hydroxy compound ( X ) with molar mass 122 ~g ~mol ⁻¹ is acetylated with acetic anhydride, using a large excess of the reagent ensuring complete acetylation of all hydroxyl groups. The product obtained has a molar mass of 290 ~g ~mol ⁻¹ . The number of hydroxyl groups present in compound (X) is:

Step-by-step solution

In acetylation, each hydroxyl group reacts: R-OH + (CH₃CO)₂O → R-O-CO-CH₃ + CH₃COOH. Each -OH is converted to -OCOCH₃, resulting in a net mass increase of 42 g/mol per hydroxyl group (addition of acetyl group mass 43, removal of hydrogen mass 1). Given: Original molar mass = 122 g/mol, Product molar mass = 290 g/mol Total mass increase = 290 - 122 = 168 g/mol Number of hydroxyl groups = 168 ÷ 42 = 4